The following is the Linear programming model for analyzing the product mix of M

The following is the Linear programming model for analyzing the product mix of Maxine’s Hat Company which produces three hat styles.
Maximize Z: $7×1 + $5×2 + $2×3
Subject to: 3×1 + 5×2 + x3 ≤ 150 (machine A time)
5×1 + 3×2 + 2×3 ≤ 100 (machine B time)
x1 + 2×2 + x3 ≤ 160 (machine C time)
A. Find the optimal solution using solver.
B. Consider each of the following statements independently and state whether you consider them true or false. Explain each answer
(i) If the price of hat 3 were increased to $2.50, it would be part of the optimal mix
(ii) The capacity of machine 3 can be reduced to 65 hours without affecting profits
(iii) If machine A had a capacity of 170 hours, the production output would remain unchanged